PSI - Issue 39

Arturo Pascuzzo et al. / Procedia Structural Integrity 39 (2022) 649–662 Author name / Structural Integrity Procedia 00 (2019) 000–000

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Keywords: Crack propagation; Finite Element Method; Moving Mesh; ALE; M-integral; Functionally Graded Materials

1. Introduction Functionally Graded Materials (FGMs) are novel composites made of two phases (usually metallic and ceramic) merged in such a way to have gradually variable volume fractions along pre-defined design directions (Shen (2016)). FGMs have several advantages, such as excellent thermal properties and no material interface. However, the ceramic phase makes them susceptible to brittle fracture. When fracture occurs, the gradual heterogeneous macro-properties affect the stress field around the crack tip, thus giving rise to complex and unpredictable crack trajectories. For this reason, reliable numerical approaches are necessary to assess the structural integrity of FGMs. In particular, accurate numerical strategies able to predict crack nucleation and propagation phenomena in FGMs are essential to achieve an exhaustive overview of structural performances, thereby identifying the major weaknesses that affect the overall integrity. Most of the numerical approaches developed for analyzing the fracture behavior of FGMs have been developed in the framework of the Finite Element Method (FEM) because of its simplicity to model articulated structures, also made of heterogeneous materials (Greco et al. (2018b), Greco et al. (2020a), Greco et al. (2021b)). However, standard FEM strategies are quite cumbersome to model crack propagation mechanisms in FGMs because of twofold reasons. First, because of the heterogeneity of the material properties of FGMs, crack paths can grow arbitrarily, thus making it impossible to predict them in advance. Therefore, the computational mesh must be updated continuously during numerical simulations through remeshing actions. Unfortunately, remeshing actions are time-consuming and increase the possibility of convergence issues during each mesh regeneration step. Second, the need to reproduce the singularity of the stress fields at the crack tip involves the use of a refined mesh configuration in the crack tip region. Alternatively, special singular finite elements can be adopted. However, in both cases, numerical models can undergo difficulties because of the relevant amount of Degree of Freedom to account for. To overcome such complexities, enhanced FEM-based strategies based on refined finite element formulations able to reproduce the crack path evolution within the computational domain have been developed. Among these, the Extended Finite Element Method (XFEM) (Comi and Mariani (2007), Bayesteh and Mohammadi (2013)) and methodologies based on Phase Field Formulations (PFF) (Hirshikesh et al. (2019), Dinachandra and Alankar (2020)) effectively reproduce crack nucleation and propagation mechanisms through finite elements without the need of remeshing actions. However, these attractive methodologies require highly refined mesh configurations to handle arbitrarily growing cracks. Besides, special computational procedures must be used because of the presence of enrichment contributions in the numerical formulation. These aspects limit the operative range of such approaches to cases made of small and quite regular geometries. In the framework of FEM-based approaches, numerical methods based on the use of Cohesive Zone Modeling (CZM) approach, originally proposed by Dugdale and Barenblatt (Dugdale (1960), Barenblatt (1962)), are frequently used as well. However, such a modeling strategy is efficient when crack paths are known in advance (e.g., debonding phenomena occurring at the interface between dissimilar materials) (Greco et al. (2020a), Pascuzzo et al. (2020)). To reproduce complex crack propagation phenomena involving arbitrarily growing cracks, continuous remeshing actions of the computational mesh must be operated, thus making the method quite cumbersome. As an alternative, diffuse interface modeling strategies can be used. Such approaches involve the insertion of interface elements along all the boundaries of the finite elements before the analysis, thereby avoiding remeshing actions and ensuring the reproduction of the nucleation and growth of cracks in a more natural manner (De Maio et al. (2019a), De Maio et al. (2019b), De Maio et al. (2020a), De Maio et al. (2020b), Greco et al. (2020b), De Maio et al. (2021)). However, the necessity of handle a relevant number of interface elements limits the applicability of strategy to fracture problems of small geometries. Recently, a novel class of hybrid numerical procedures has risen (Greco et al. (2020c)). Such approaches join the strengths of classic methodologies to configure enhanced procedures able to ensure reliable predictions and optimal computational performances. As an example of a hybrid approach, the Scaled Boundary Finite Element Method (SB ‐ FEM) (Ooi et al. (2015)) combines the flexibility of the FEM and the computational efficiency of the Boundary Element Method (BEM) strengths to manage mesh updates.